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Background: There are insufficient studies on the effect of dietary salt intake on cardiovascular (CV) outcomes in chronic kidney disease (CKD) patients, and there is no consensus on the sodium (Na) intake level that increases the risk of CV disease in CKD patients. Therefore, we investigated the association between dietary salt intake and CV outcomes in CKD patients. Methods: In the Korean cohort study for Outcome in patients with CKD (KNOW-CKD), 1,937 patients were eligible for the study, and their dietary Na intake was estimated using measured 24h urinary Na excretion. The primary outcome was a composite of CV events and/or all-cause death. The secondary outcome was a major adverse cardiac event (MACE). Results: Among 1,937 subjects, there were 205 (10.5%) events for the composite outcome and 110 (5.6%) events for MACE. Compared to the reference group (urinary Na excretion< 2.0g/day), the group with the highest measured 24h urinary Na excretion (urinary Na excretion ≥ 8.0g/day) was associated with increased risk of both the composite outcome (hazard ratio 3.29 [95% confidence interval 1.00-10.81]; P = 0.049) and MACE (hazard ratio 6.28 [95% confidence interval 1.45-27.20]; P = 0.013) in a cause-specific hazard model. Subgroup analysis also showed a pronounced association between dietary salt intake and the composite outcome in subgroups of patients with abdominal obesity, female, lower estimated glomerular filtration rate (< 60 ml/min per 1.73m2), no overt proteinuria, or a lower urinary potassium-to-creatinine ratio (< 46 mmol/g). Conclusion: A high-salt diet is associated with CV outcomes in non-dialysis CKD patients.
RESUMO
This paper tackles linear programming problems with data uncertainty and applies it to an important inventory control problem. Each element of the constraint matrix is subject to uncertainty and is modeled as a random variable with a bounded support. The classical robust optimization approach to this problem yields a solution with guaranteed feasibility. As this approach tends to be too conservative when applications can tolerate a small chance of infeasibility, one would be interested in obtaining a less conservative solution with a certain probabilistic guarantee of feasibility. A robust formulation in the literature produces such a solution, but it does not use any distributional information on the uncertain data. In this work, we show that the use of distributional information leads to an equally robust solution (i.e., under the same probabilistic guarantee of feasibility) but with a better objective value. In particular, by exploiting distributional information, we establish stronger upper bounds on the constraint violation probability of a solution. These bounds enable us to "inject" less conservatism into the formulation, which in turn yields a more cost-effective solution (by 50% or more in some numerical instances). To illustrate the effectiveness of our methodology, we consider a discrete-time stochastic inventory control problem with certain quality of service constraints. Numerical tests demonstrate that the use of distributional information in the robust optimization of the inventory control problem results in 36%-54% cost savings, compared to the case where such information is not used.
